Measurement of the differential cross section of $t\bar{t}$ production, using data collected by the ATLAS detector at $\sqrt{s}$ = 13 TeV

The study of the top quark physics covers a large part of the ATLAS experiment physics program and represents an active research field for the theoretical community. In this thesis, the measurement of the differential cross-sections of top quark pair production in proton proton collisions at a centre of mass energy of $\sqrt{s}=13$ TeV is presented. The measurement is performed in a fiducial phase-space, as a function of top quark and $t\bar{t}$ system kinematic observables, and the data set corresponds to an integrated luminosity of 3.2 $\mathrm{fb}^{-1}$, recorded in 2015 with the ATLAS detector at the CERN Large Hadron Collider. Only events with exactly one electron or muon in the final state are retained and the analysis employs two separate selections and top quark reconstruction techniques, focusing on different regions of the top quark momentum spectra. The measured spectra are corrected for detector effects and are compared to several theoretical Monte Carlo simulations through $\chi^2$ and $p$-values calculations. The measured spectra provide stringent tests of perturbative QCD and can be used to tune the Monte Carlo simulations and re-interpreted to set limits on the existence of processes beyond the standard model. Finally, new techniques that will improve the sensitivity of future analysis in the region where the top quark is produced with high transverse momentum are presented.